Pulse compression radar systems utilize waveforms that have narrow autocorrelation functions and time-bandwidth (TB) products that are much higher than unity enabling good range resolution (bandwidth dependent) and target detection (energy dependent). In operation, a known electromagnetic pulse is transmitted from a transmitting device, e.g., a transmitter or transceiver, and the transmitted pulse reflects off an object. The reflected signal is received at the receiver or transceiver and undergoes various signal processing techniques including signal pulse compression.
FIG. 1 illustrates one example of a conventional matched filter (cross-correlation) processing channel 100 for pulse compressing waveforms. As shown in FIG. 1, a received signal undergoes a fast Fourier transform (FFT) at block 102 to transform the received signal from the time domain to the frequency domain. Similarly, the reference signal is fast Fourier transformed at block 108 to transform the reference signal into the frequency domain. At block 110, the complex conjugate of the transformed reference is taken and multiplied with the transform of the received signal at block 104. The product of the multiplication performed at block 104 undergoes an inverse FFT (IFFT) at block 106 to convert the product back to the time domain. The output of the IFFT 106 is the matched filter output. However, the matched filter output from the conventional processing channel 100 exhibits intolerance to a Doppler shift unless the transmitted signal is weighted. The graphical result of a cross-correlation is illustrated in FIG. 2, which shows a composite function including a mainlobe 10 and a plurality of sidelobes 20. In contrast to the composite function illustrated in FIG. 2, an ideal autocorrelation function will have a mainlobe width of zero and zero sidelobes. However, practical finite-duration and finite-bandwidth waveforms have non-zero autocorrelation widths and finite sidelobe levels, which limit the target dynamic range. The limited dynamic range may have a negative effect on the radar system as a weaker target may be located in one of sidelobes and therefore avoid being detected.
NLFM waveforms have lower peak sidelobe levels (PSLs) and do not incur losses due to weighting compared to linear frequency modulated (LFM) waveforms. Additionally, NLFM waveforms have a constant-amplitude envelope, which enables efficient generation of high power signals, with a continuous phase so that they are spectrally well contained. Accordingly, these features have led to the implementation of NLFM waveforms in pulse compression radar systems for tracking targets.
However, the pulsed compressed output of NLFM waveforms degrades if there is an uncompressed Doppler shift. Specifically, the mainlobe widens and the PSL increases. The Doppler intolerance of NLFM waveforms is illustrated in FIGS. 3A-3D, which are graphs of the NLFM signal strength versus range for stationary (lines 300) and moving targets, e.g., targets moving at Mach 1 (lines 301), Mach 2 (lines 302), and Mach 3 (lines 303), in radar systems having various TB products. Specifically, FIG. 3A illustrates the NLFM waveforms for a system having a TB product equal to 16; the waveforms illustrated in FIG. 3B are for a system having a TB product equal to 64; the waveforms illustrated in FIG. 3C is for a system having a TB product of 256; and the waveforms illustrated in FIG. 3D are for a system having a TB of 1024. FIGS. 3A-3D show that as the TB product is increased from 16 to 1024, the NLFM waveforms experience an increasingly larger Doppler shift causing the distortion to the right of the mainlobe for targets moving at Mach 1 (i.e., the speed of sound), Mach 2 (i.e., twice the speed of sound), and Mach 3 (i.e., three times the speed of sound).
Hybrid NLFM processing has been developed in an attempt to compensate for the Doppler shift experienced by NLFM waveforms. An example of Hybrid processing is disclosed by Collins et al. in Nonlinear Frequency Modulation Chirps for Active Sonar, IEEE Proc. Radar, Sonar, and Navigation, Vol. 146, No. 6, December 1999, pp 312-316, the entirety of which is incorporated by reference herein. In Hybrid NLFM systems, the NLFM waveform is designed using the principle of stationary phase and a frequency weighting function such as Taylor weighting. The resultant waveform does not experience mismatch loss if pulse-compressed; however, the waveform will experience weighting loss. While Hybrid NLFM provides some Doppler tolerance, it does so at the expense of resolution as due to the weighting loss.
Accordingly, an improved system and method for processing NLFM waveforms are desirable.